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Title: The continuous spectrum and the effect of parametric resonance. The case of bounded operators

The paper is concerned with the Mathieu-type differential equation u{sup ″}=−A{sup 2}u+εB(t)u in a Hilbert space H. It is assumed that A is a bounded self-adjoint operator which only has an absolutely continuous spectrum and B(t) is almost periodic operator-valued function. Sufficient conditions are obtained under which the Cauchy problem for this equation is stable for small ε and hence free of parametric resonance. Bibliography: 10 titles.
Authors:
 [1]
  1. S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)
Publication Date:
OSTI Identifier:
22365154
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 5; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CAUCHY PROBLEM; DIFFERENTIAL EQUATIONS; FUNCTIONS; HILBERT SPACE; MATHEMATICAL SOLUTIONS; PERIODICITY; RESONANCE